NEW ORLEANS — The New Orleans Saints have the longest winning streak in the NFL.

It’s hard to predict when it might end.

It reached seven games when the Saints beat the Los Angeles Rams 45-35 on Sunday in the Mercedes-Benz Superdome.

It became the longest in the league at the expense of the Rams, who entered the game with an 8-0 record.

“There is no derailing this train,” said running back Alvin Kamara, who displayed a few locomotive-like traits of his own in matching a career-high with three touchdowns.

The Rams couldn’t keep up in a game that they never led.

Drew Brees passed for 346 yards and four touchdowns a week after he needed just 120 passing yards in a 30-20 victory at Minnesota.

The offensive line prevented Brees from being sacked for a second consecutive week as it reached the mid-point of the season having allowed an NFL-low nine sacks.

Brees connected 12 times with Michael Thomas, who set a franchise record with 211 receiving yards. One of the connections was a 72-yard touchdown on a third-and-7, which gave New Orleans a 10-point lead with less than five minutes remaining.

And that in a nutshell is the dilemma opposing defenses are facing — how to defend Kamara and Thomas. Even as Thomas was making all those catches for all those yards, Brees was able to connect with eight other receivers.

There was a 16-yard touchdown pass to Kamara, a 4-yard touchdown to rookie Tre’Quan Smith and a 13-yard touchdown to tight end Benjamin Watson.

“You can see why Drew is a first-ballot Hall of Famer,” L.A. coach Sean McVay said.

Brees, who had his seventh interception-free game out of eight, led the Saints to 487 yards, their most in a regulation game this season, as they gained 31 first downs. They broke their own NFL record for first downs in a first half with 24.

But there’s much more to this offense than just Brees and the passing game and much more to this team than just the offense.

Kamara and Mark Ingram II led the way as New Orleans rushed for 141 yards, 49 more than the NFL’s top rushing team, which was held to its second-lowest total of the season by the Saints defense. Todd Gurley II, the NFL’s leading rusher had 68 yards, 32 below his average.

The Rams accumulated 483 yards and scored 21 unanswered points to pull even in the fourth quarter after the Saints had raced to a 35-14 second-quarter lead. But the New Orleans defense did enough to complement the offense and the special teams. Alex Anzalone’s intercepted Jared Goff, leading to a touchdown that completed the Saints’ own 21-0 blitz in the second quarter.

Though Goff drove the Rams to touchdowns on their first two possessions of the game, they managed just three points on their final four possessions of the first half.

The most significant sequence occurred early in the second quarter. The score was tied at 14 when Ingram lost a fumble at the New Orleans 22.

The defense allowed just six yards in three plays and McVay sent in the field-goal team. The Rams ran a fake and holder Johnny Hekker ran to the right side, where he saw some room toward the sideline.

But linebacker Craig Robertson ran him down at the sideline, just short of the first down. The spot was upheld on replay after McVay challenged.

“That was a huge stop,” Payton said, “because we had just had the turnover.”

Brees drove the Saints 87 yards to a touchdown and they were off and running.

Eventually L.A. would pull even, but Wil Lutz’s season-long 54-yard field goal preceded the Brees-Thomas touchdown, which ended with Thomas drawing an unsportsmanlike conduct penalty for pulling out a cell phone in the same end zone where former Saint Joe Horn famously did so in a prime-time game 17 years earlier.

“I wasn’t all fired up about the penalty,” Payton said. “We’ll get that figured out and handled. But (Thomas) had a good game.”

The defense finished the second half as strongly as it did the first, holding L.A. scoreless on its final two possessions.

“They made the critical plays at the end,” McVay said.

The Saints are making a habit of that.

After opening the season with an upset loss at home against Tampa Bay, they rallied late to escape with a 21-18 home victory against Cleveland after the Browns missed a series of place kicks in the fourth quarter.

Then came an overtime win at Atlanta and a methodical win at the Giants.

Since then, it has been a series of victories against teams that were leading their division when they met the Saints — Washington, Baltimore, Minnesota and now Los Angeles.

“I felt coming in that we were battle tested,” Payton said, “and that served us well.”